Collapse of nonlinear gravitational waves in moving-puncture coordinates

Abstract

We study numerical evolutions of nonlinear gravitational waves in moving-puncture coordinates. We adopt two different types of initial data -Brill and Teukolsky waves -and evolve them with two independent codes producing consistent results. We find that Brill data fail to produce long-term evolutions for common choices of coordinates and parameters, unless the initial amplitude is small, while Teukolsky wave initial data lead to stable evolutions, at least for amplitudes sufficiently far from criticality. The critical amplitude separates initial data whose evolutions leave behind flat space from those that lead to a black hole. For the latter we follow the interaction of the wave, the formation of a horizon, and the settling down into a time-independent trumpet geometry. We explore the differences between Brill and Teukolsky data and show that for less common choices of the parameters -in particular negative amplitudes -Brill data can be evolved with moving-puncture coordinates, and behave similarly to Teukolsky waves.

Black hole critical behavior with the generalized BSSN formulation

“…However, their original results have proven very difficult to reproduce (or refute) [28][29][30][31]34]. We refer the reader to the recent paper by Hilditch et al [34] for detailed discussions concerning some apparent inconsistencies among the follow-up studies, as well as the challenges and complications involved in evolving various types of nonlinear gravitational waves. We are currently extending the methodology described above to the axisymmetric case with plans to use the resulting code to study vacuum collapse.…”

“…Given (32)(33)(34)(35), the G-BSSN equations become a set of first order evolution equations for the 7 primary variables φ(t, r),γ rr (t, r),γ θθ (t, r), K(t, r),…”

Critical phenomena in the aspherical gravitational collapse of radiation fluids

“…In addition to studying critical phenomena in the aspherical collapse of radiation fluids, this paper serves as a demonstration that an unconstrained evolution code, using "movingpuncture" coordinates, is suitable for the study of critical collapse, at least for some matter models (see also [10,23,24] for recent discussions of this issue.) We denote gridpoints with r i and define…”

“…(8) and (9) below) have proven particularly useful for simulations of spacetimes containing black holes. How suitable these codes are for simulations of critical collapse, however, remains a somewhat open question (see also [10,23,24] for recent discussions.) Our findings here demonstrate that, at least for some matter models, unconstrained evolution codes with the 1+log and Gamma-driver coordinate conditions can indeed be used to study critical phenomena.…”

Numerical relativity in spherical polar coordinates: Off-center simulations

“…Because different parts of the code are differenced to different order, the order of convergence depends on which term dominates the error for the variable under consideration. In [27] we also used this code to simulate the collapse of nonlinear gravitational waves to black holes.…”